You’re not going to be done with anything, really, though. Coyotes are pervasive throughtout the west. They’re definitely going to be taking pets that are left outside. Mountain lions will do the same thing. Maltese and Shih-tzus are not exactly difficult meals.
I guess it depends on how densely the area is populated. Hunting them to thin the population is generally a good idea. It also reinstalls a fear of man in them, which a bunch of urbanite idiots can’t seem to comprehend. The Californians who moved to Colorado will raise chaos if someone starts shooting coyotes, for instance.
Sounds to me that the lions are providing a community service.